Answer: [tex]\dfrac{13}{21}[/tex]
Step-by-step explanation:
The given table :
Boys Girls
Juniors 6 8
Seniors 16 12
Let G denote the event of choosing girl and J denote the event of choosing Junior.
Number of girls : 8+12=20
Number of Juniors : 6+8=14
Members that are girl and junior = 8
Total students : 6+8+16+12=42
The probability of choosing girl is given by :-
[tex]P(G)=\dfrac{20}{42}[/tex]
The probability of choosing junior is given by :-
[tex]P(J)=\dfrac{14}{42}[/tex]
The probability of choosing a girl and junior is given by ;-
[tex]P(G\cap J)=\dfrac{8}{42}[/tex]
Now, the probability choosing a girl or a junior is given by :-
[tex]P(G\cup J)=P(G)+P(J)-P(G\cap J)\\\\=\dfrac{20}{42}+\dfrac{14}{42}-\dfrac{8}{42}\\\\=\dfrac{26}{42}=\dfrac{13}{21}[/tex]
Hence, the probability that Annie chooses a girl or a junior= [tex]\dfrac{13}{21}[/tex]
